F(x)=-8x^2-7x+7

Solution for F(x)=-8x^2-7x+7 equation:

(F)=-8F^2-7F+7

We move all terms to the left:

(F)-(-8F^2-7F+7)=0

We get rid of parentheses

8F^2+7F+F-7=0

We add all the numbers together, and all the variables

8F^2+8F-7=0

a = 8; b = 8; c = -7;
Δ = b2-4ac
Δ = 82-4·8·(-7)
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{2}}{2*8}=\frac{-8-12\sqrt{2}}{16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{2}}{2*8}=\frac{-8+12\sqrt{2}}{16}
$